Dynamical Critical Exponent for Two-Species Totally Asymmetric Diffusion on a Ring

TL;DR

This paper investigates a two-species asymmetric diffusion model using Bethe ansatz, revealing a dynamical critical exponent of 3/2, consistent with KPZ universality class, and extends understanding of multi-species non-equilibrium systems.

Contribution

It derives nested Bethe ansatz equations for the two-species model and determines its dynamical critical exponent from finite-size scaling analysis.

Findings

Dynamical critical exponent is 3/2.

Model exhibits KPZ universality class behavior.

Provides Bethe ansatz solution for two-species diffusion.

Abstract

We present a study of the two species totally asymmetric diffusion model using the Bethe ansatz. The Hamiltonian has $U_q(SU(3))$ symmetry. We derive the nested Bethe ansatz equations and obtain the dynamical critical exponent from the finite-size scaling properties of the eigenvalue with the smallest real part. The dynamical critical exponent is 3/2 which is the exponent corresponding to KPZ growth in the single species asymmetric diffusion model.